Electronic Journal of Differential Equations,
Vol. 2007(2007), No. 12, pp. 1-14.
Title: Boundedness and exponential stability of solutions
to dynamic equations on time scales
Author: Ai-Lian Liu (Shandong Economics Univ., China)
Abstract:
Making use of the generalized time scales exponential function,
we give a new definition for the exponential stability of solutions
for dynamic equations on time scales. Employing Lyapunov-type
functions on time scales, we investigate the boundedness and the
exponential stability of solutions to first-order dynamic equations
on time scales, and some sufficient conditions are obtained.
Some examples are given at the end of this paper.
Submitted January 16, 2006. Published January 8, 2007.
Math Subject Classifications:
Key Words: Time scale; Lyapunov-type function on time scales;
boundedness; exponential stability.